Determine the expansion coefficients of a function for a given set of input Slepian functions.

## Usage

call SlepianCoeffs(falpha, galpha, flm, lmax, nmax, exitstatus)

## Parameters

falpha : output, real*8, dimension (nmax)
A vector containing the Slepian coefficients of the input function flm.
galpha : input, real*8, dimension ((lmax+1)**2, nmax)
An array containing the spherical harmonic coefficients of the Slepian functions. Each column corresponds to a single function of which the spherical harmonic coefficients can be unpacked with SHVectorToCilm.
flm : input, real*8, dimension (2, lmax+1, lmax+1)
The spherical harmonic coefficients of the global function to be expanded in Slepian functions.
lmax : input, integer
The spherical harmonic bandwidth of the Slepian functions.
nmax : input, integer
The number of expansion coefficients to compute.
exitstatus : output, optional, integer
If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.

## Description

SlepianCoeffs will compute the Slepian coefficients of a global input function flm given the Slepian functions galpha. The Slepian functions are determined by a call to either (1) SHReturnTapers and then SHRotateTapers, or (2) SHReturnTapersMap. Each row of galpha contains the (lmax+1)**2 spherical harmonic coefficients of a Slepian function that can be unpacked using SHVectorToCilm. The Slepian functions must be normalized to have unit power (that is the sum of the coefficients squared is 1), and the Slepian coefficients are calculated as

f_alpha = sum_{lm}^{lmax} f_lm g(alpha)_lm